Silicon, which occurs in nature as SiO2, is the material from which most computer chips are made. If SiO2 is heated until it melts into a liquid, it reacts with solid carbon to form liquid silicon and carbon monoxide gas. In an industrial preparation of silicon, 52.8 kg of SiO2 reacts with 25.8 kg of carbon to produce 22.4 kg of silicon. Determine the limiting reactant, theoretical yield, and percent yield for the reaction.
Balanced equation: SiO2 + 2 C -> Si + 2 CO
1. Find the moles of each:
Grams -> moles
Given kg x 1000 g/1 kg x 1 mol/molar mass
Molar mass SiO2: 60.08 g/mol
Molar mass C: 12.01 g/mol
57.8 kg SiO2 x 1000 g SiO2/1 kg SiO2 x 1 mol SiO2/60.08 g SiO2 = 962.05 mol SiO2
25.8 kg C x 1000 g C/1 kg C x 1 mol C/12.01 g C = 2148.21 mol C
2. Then using the balanced equation, set up a mole ratio: Coefficients/Number of moles.
1 SiO2/962.05 mol SiO2 = 2 C/x
We pretend we don't know the moles of C.
By crossing multiplying, we find x = 1924.1 mol C, which is less than 2148.21 mol C. This tells us we will have EXTRA C, and that SiO2 is our limiting reactant.
We find the theoretical yield by doing a regular stoichiometry problem:
Molar ratio: 1 mol SiO2 : 1 mol Si
Molar mass Si: 28.09 g/mol
57.8 kg SiO2 x (1000 g SiO2/1 g SiO2) x (1 mol SiO2/60.08 g SiO2) x (1 mol Si/1 mol SiO2) x (28.09 g Si/1 mol Si) x 1 kg Si/1000 g Si = 27.024 kg Si
Sig figs... 27.0 kg Si
The percent yield can be found using the following equation:
mass of actual yield/mass of theoretical yield x 100%
Mass of actual yield: 22.4 kg
Mass of theoretical yield: 27.0 kg
22.4/27.0 x 100% = 82.963%
Sig figs... 83.0%